Finite Quantum Tomography and Semidefinite Programming

Using the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: truncated coherent states tomography, phase tomography and coherent spin state tomography, qudit tomography, N-qubit tomography, where that obtained results are in agreement with those of References (Buzek et al., Chaos, Solitons and Fractals 10 (1999) 981; Schack and Caves, Separable states of N quantum bits. In: Proceedings of the X. International Symposium on Theoretical Electrical Engineering, 73. W. Mathis and T. Schindler, eds. Otto-von-Guericke University of Magdeburg, Germany (1999); Pegg and Barnett Physical Review A 39 (1989) 1665; Barnett and Pegg Journal of Modern Optics 36 (1989) 7; St. Weigert Acta Physica Slov. 4 (1999) 613). PACs index: 03.65.Ud     

Parameter identification of chaos system based on unknown parameter observer

Parameter identification of chaos system based on unknown parameter observer is discussed generally. Based on the work of Guan et al. [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26], the design of unknown parameter observer is improved. The application of the improved approach is extended greatly. The works in some literatures [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26; J.H. Lü, S.C. Zhang, Phys. Lett. A 286 (2001) 148; X.Q. Wu, J.A. Lu, Chaos Solitons Fractals 18 (2003) 721; J. Liu, S.H. Chen, J. Xie, Chaos Solitons Fractals 19 (2004) 533] are only the special cases of our Corollaries 1 and 2. Some observers for Lü system and a new chaos system are designed to test our improved method, and simulations results demonstrate the effectiveness and feasibility of the improved approach.     

Schwarzian derivative as a proof of the chaotic behaviour

In recent years, a sufficient condition for determining chaotic behaviours of the non-linear systems has been characterized by the negative Schwarzian derivative (Hac?bekiro?lu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame of reference, which is known as a nonlinear dynamical system that displays some macroscopic quantum effects. In our previous works, two quantum chaotic transition points of the critical transition temperature, T _c, and paramagnetic Meissner transition temperature, T _PME, have been phenomenologically predicted for the mercury-based high-temperature superconductors (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009); Aslan et al, J. Phys.: Conf. Ser. 153, 012002 (2009); Çataltepe, Superconductor (Sciyo Company, India, 2010)). The T _c, at which the one-dimensional global gauge symmetry is spontaneously broken, refers to the second-order phase transition, whereas the T _PME, at which time reversal symmetry is broken, indicates the change in the direction of orbital current in the system (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009)). In this context, the chaotic behaviour of the mercury-based high-temperature superconductors has been investigated by means of the Schwarzian derivative of the magnetic moment versus temperature. In all calculations, the Schwarzian derivatives have been found to be negative at both T _c and T _PME which are in agreement with the chaotic behaviour of the system.     

Comment on: “A simple chaotic delay differential equation” [Phys. Lett. A 366 (2007) 397]

The purpose of this Letter is to give the reference for the model proposed in the discussion section of the above paper [J.C. Sprott, Phys. Lett. A 366 (2007) 397] and to show that chaotic behavior of this model has been studied in [A. Uçar, Int. J. Eng. Sci. 40 (2002) 251; A. Uçar, Chaos Solitons Fractals 16 (2003) 187].     

Single-oscillator model and determination of optical constants of spray pyrolyzed amorphous SnO<Subscript>2</Subscript> thin films

It has recently been shown that growth of a multilayer structure with one or more delta-layers at high temperature leads to spreading and asymmetrization of the dopant distribution [see, for example, E.F.J. Schubert, Vac. Sci. Technol. A. 8, 2980 (1990), A.M. Nazmul, S. Sugahara, M. Tanaka, J. Crystal Growth 251, 303 (2003); R.C. Newman, M.J. Ashwin, M.R. Fahy, L. Hart, S.N. Holmes, C. Roberts, X. Zhang, Phys. Rev. B 54, 8769 (1996); E.F. Schubert, J.M. Kuo, R.F. Kopf, H.S. Luftman, L.C. Hopkins, N.J. Sauer, J. Appl. Phys. 67, 1969 (1990); P.M. Zagwijn, J.F. van der Veen, E. Vlieg, A.H. Reader, D.J. Gravesteijn, J. Appl. Phys. 78, 4933 (1995); W.S. Hobson, S.J. Pearton, E.F. Schubert, G. Cabaniss, Appl. Phys. Lett. 55, 1546 (1989); Delta Doping of Semiconductors, edited by E.F. Schubert (Cambridge University Press, Cambridge, 1996); Yu.N. Drozdov, N.B. Baidus', B.N. Zvonkov, M.N. Drozdov, O.I. Khrykin, V.I. Shashkin, Semiconductors 37, 194 (2003); E. Skuras, A.R. Long, B. Vogele, M.C. Holland, C.R. Stanley, E.A. Johnson, M. van der Burgt, H. Yaguchi, J. Singleton, Phys. Rev. B 59, 10712 (1999); G. Li, C. Jagadish, Solid-State Electronics 41, 1207 (1997)]. In this work analytical and numerical analysis of dopant dynamics in a delta-doped area of a multilayer structure has been accomplished using Fick's second law. Some reasons for asymmetrization of a delta-dopant distribution are illustrated. The spreading of a delta-layer has been estimated using example materials of a multilayer structure, a delta-layer and an overlayer.     

Evolution of the initial box-signal for time-fractional diffusion-wave equation in a case of different spatial dimensions

In the case of time-fractional diffusion-wave equation considered in the spatial domain −∞<x<∞, evolution of initial box-signal was investigated by Mainardi [F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos Solitons Fractals 7 (1996) 1461-1477]. In the present paper, we supplement Mainardi’s results with additional numerical calculations illustrating the behavior of the solution and solve the corresponding problems for axisymmetric and central symmetric cases. The obtained results show an unusual behavior of solutions.     

Quantum diffusion in bilateral doped chains

In this paper,we quantitatively study the quantum diffusion in a bilateral doped chain,which is randomly doped on both sides.A tight binding approximation and quantum dynamics are used to calculate the three electronic characteristics:autocorrelation function C(t),the mean square displacement d(t) and the participation number P (E) in different doping situations.The results show that the quantum diffusion is more sensitive to the small ratio of doping than to the big one,there exists a critical doping ratio q 0,and C(t),d(t) and P (E) have different variation trends on different sides of q 0.For the self-doped chain,the doped atoms have tremendous influence on the central states of P (E),which causes the electronic states distributed in other energy bands to aggregate to the central band (E=0) and form quasi-mobility edges there.All of the doped systems experience an incomplete transition of metal-semiconductor-metal.     

New Soliton-like Solutions and Multi-soliton Structures for Broer-Kaup System with Variable Coefficients

By using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669] to the Broer-Kaup system with variable coefficients, abundant new soliton-like solutions and multl-solitonlike solutions are derived. Based on the derived multi-soliton-like solutions which contain arbitrary functions, some interesting multi-soliton structures are revealed.     

New Exact Solutions to （2＋1）-Dimensional Dispersive Long Wave Equations

Based upon a further extended tanh method [Phys. Lett. A307 (2003) 269; Chaos, Solitons and Fractals 17 (2003) 669] and the symbolic computation system, Maple, we consider the (2 1)-dimensional dispersive long waveequations. We obtain many new solutions of the equation. These solutions contain solitomlike solutions, periodic form solutions, and some rational solutions.     

Transport of intense beams of highly charged ions

The new generation of ion sources delivers beams with intensities of several mA. This requires a careful design of the analysing system and the low-energy beam transport (LEBT) from the source to the subsequent systems. At INFN-LNS, high intensity proton sources (TRIPS [L. Celona, G. Ciavola, S. Gammino et al., Rev. Sci. Instrum. 75(5) 1423 (2004)], PM-TRIPS [G. Ciavola, L. Celona, S. Gammino et al., Rev. Sci. Instrum. 75(5) 1453 (2004)]) as well as ECR ion sources for the production of highly charged high-intensity heavy ion beams are developed (SERSE [S. Gammino, G. Ciavola, L. Celona et al., Rev. Sci. Instrum. 72(11) 4090 (2001), and references therein], GyroSERSE [S. Gammino et al., Rev. Sci. Instrum. 75(5) 1637 (2004)], MS-ECRIS [G. Ciavola et al., (2005), 11th Int. Conf. on Ion Sources, Caen, (in press)]).

In this paper, we present ion-optical design studies of various LEBT systems for ion-sources devoted to the production of intense beams. Calculations were performed using the computer codes GIOS [H. Wollnik, J. Brezina and M. Berz, NIM A 258 (1987)], GICO [M. Berz, H.C. Hoffmann, and H. Wollnik, NIM A 258 (1987)], and TRANSPORT [K.L. Brown, F. Rothacker and D.C. Carey, SLAC-R-95-462, Fermilab-Pub-95/069, UC-414 (1995)]. Simulations take into account the expected phase space growth of the beam emittance due to space-charge effects and image aberrations introduced by the magnetic elements.     

Influence of local nonequilibrium on the rapid solidification of binary alloys

A local-nonequilibrium model of the diffusion of a solute during the rapid solidification of a binary alloy is considered. The model has two characteristic parameters: the diffusion velocity through the interface V _Di and the diffusion velocity in the bulk of the liquid phase V _D. The influence of local nonequilibrium on the separation of an impurity, the stability of the interface, and the dependence of the temperature of the interface on the velocity of the solidification front is investigated. A comparison with experiment is made. Zh. Tekh. Fiz. 68, 45–52 (March 1998)     

Two-Particle Irreducible Effective Action in Gauge Theories

The goal of this paper is to develop the formalism of the two-particle irreducible (2PI) (G. Baym (1962). Physical Review 127, 1391; H. D. Dahmen and G. Jona Lasino (1962). Nuovo Cimento A 52, 807; C. de Dominicis and P. Martin (1964). Journal of Mathematical Physics 5, 14; J. Luttinger and J. Ward (1960). Physical Review 118, 1417; B. Vanderheyden and G. Baym (1998). Journal of Statistical Physics 98, 843; B. Vanderheyden and G. Baym (2000). In Progress in Nonequilibrium Green's Functions, World Scientific, Singapore). (or Cornwall–Jackiw–Tomboulis (CJT) (J. Cornwall, R. Jackiw, and E. Tomboulis (1974). Physical Review D 10, 2428; U. Kraemmer and A. Rebhan (2004). Reports on Progress in Physics 67, 351; R. Norton and J. Cornwall (1975). Annals of Physics 91, 106) effective action (EA) in a way appropiate to its application to nonequilibrium gauge theories. We hope this review article will stimulate new work into this field.     

On the relation between a fluctuating diffusion equation and long time tails in stationary random media

Ernst, Machta, Dorfman, and van Beijeren [J. Stat. Phys. 34:477 (1984);35:413 (1984)] have proposed that diffusion in a stationary random medium is described by a fluctuating diffusion equation involving a coarse-grained local diffusion coefficient K(r) and free volume fraction(r). We show that for a particular class of models [lattice diffusion with random transition rates and constant(r)], their prediction for the long time tail in the velocity autocorrelation function is the correct asymptotic limit.     

Validity of diffusion theory in radio frequency breakdown in molecular gases in longitudinal magnetic field

The breakdown of a gas excited by a radio frequency voltage of frequency 5.6 MHz has been studied in a cylindrical discharge tube 7.2 cm long and 2.9 cm in dia and fitted with two internal electrodes at a distance of 2.5 cm in hydrogen, oxygen and air within the pressure range of a few microns to 2 torr in the presence of a longitudinal magnetic field varying from zero to 800 G. Experimental results indicate that the breakdown is diffusion controlled and the values of (a/P) at differentE/P values calculations obtained by Brown as well as by Kihara’s theory have been compared with (a/P) values obtained in the literature. It is concluded that the diffusion theory is also valid when the frequency of the exciting voltage is scaled down to radio frequency provided the collision frequency is much higher than the exciting frequency. The change of diffusion length in the presence of longitudinal magnetic field has been obtained from measuredE/P values and comparison with theoretical values indicates that there is quantitative agreement for small (H/P) values whereH is the magnetic field. The calculated values of pressure at which the breakdown voltage shows a minimum in the presence of magnetic field is in very good agreement with experimental values. It is concluded that in the presence of magnetic field also the loss of electrons takes place predominantly by the process of diffusion.     

Influence of isotopic substitution on the diffusion and thermal diffusion coefficient of binary liquids

The mutual mass diffusion coefficient (D) and the thermal diffusion coefficient ( D _T) of the liquids acetone, benzene, benzene-d ₁, benzene-d ₃, benzene-d ₅, benzene-d ₆, benzene- ¹³C₆, n-hexane, toluene, 1, 2, 3, 4-tetrahydronaphtalene, isobutylbenzene, and 1, 6-dibromohexane in protonated and perdeuterated cyclohexane have been measured with a transient holographic grating technique at a temperature of 25 ^°C. The mass diffusion coefficient shows a pronounced concentration dependence. Perdeuteration of cyclohexane only leads to marginal changes of the mass diffusion coefficient. The Stokes-Einstein equation describes the limiting tracer diffusion coefficients well if the solute molecule is smaller than the solvent. It is not capable to describe the small isotope effect of a few percent. On the other hand, the isotope effect, which is independent of concentration, is in agreement with the Enskog theory, that does not provide the absolute value of the mass diffusion coefficient of the liquid mixtures. The thermal diffusion coefficient of all the binary mixtures shows a moderate and almost linear concentration dependence. Its isotope effect, which is the change of D _T upon deuteration of cyclohexane, varies with mole fraction. The thermophoretic force acting on any tracer molecule in cyclohexane changes by the same amount when cyclohexane is perdeuterated, irrespective of the magnitude of the thermophoretic force before deuteration. This change of the thermophoretic force is equal but of opposite sign to the difference between the thermophoretic forces acting on cyclohexane and perdeuterated cyclohexane as tracers in any of the above liquids.     

Extended Complex tanh-Function Method and Exact Solutions to (2+1)-Dimensional Hirota Equation

In this paper,a new extended complex tanh-function method is presented for constructing traveling wave,non-traveling wave,and coefficient functions' soliton-like solutions of nonlinear equations.This method is nore powerful than the complex tanh-function method [Chaos,Solitons and Fractals 20 (2004) 1037].Abundant new solutions of (2 1)-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.     

Absorption lines of HLi2 by operator-ket expansion

The aim of this paper is twofold. We wish to explain and test an analytical method for calculating the matrix elements of linear operators, that simplifies the numerical calculation to mere bookkeeping. The method has been described in Huber, D., 1985, Int. J. quant. Chem., 27, 245 [1] and applied there to the general Watson-rotation-vibration hamiltonian for non-linear molecules. In this paper we want to show that the method can also be used in more complex cases. As an example we present an application to the calculation of the first electronic transition in Li₂H. The second aim is to report a calculation of the absorption spectrum of Li₂H and the discussion of its rotation-vibration states.     

Thermal diffusion of envelope solitons on anharmonic atomic chains

We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[x _s ] which predicts a stronger than linear time dependence of Var[x _s ] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales.Received: 28 June 2004, Published online: 26 November 2004PACS: 05.10.Gg Stochastic analysis methods - 05.45.Yv Solitons - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics     

Transport as a consequence of state-dependent diffusion

Overdamped particles subject to a drift in a force field with sinusoidal space dependence and also a sinusoidally modulated space-dependent diffusion, with the same period as the drift, experience a net driving force. The resulting current depends on the amplitude of the modulation of the diffusion and is a periodic function of the phase difference between the sinusoidal drift and the sinusoidal modulation of the diffusion. For small modulation amplitudes a particle subject to state-dependent noise behaves the same way as a particle subject to thermal noise but with a drift which, in addition to the sinusoidal term, contains a net force term [M. Büttiker,Z. Phys. B 68:161 (1987)]. A specific example of this behavior [N. G. van Kampen,IBM J. Res. Dev. 32:107 (1988); R. Landauer,J. Stat. Phys. 53:233 (1988).] is the motion of overdamped particles in a ring subject to a nonuniform temperature field. When the drift and the temperature, which are periodic with a period equal to the ring circumference, are not in phase a noise-induced circulating current results.This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Kinesin and the Crooks fluctuation theorem

The thermal efficiency of the kinesin cycle at stalling is presently a matter of some debate, with published predictions ranging from 0 [Phys. Rev. Lett. 99, 158102 (2007); Phys. Rev. E 78, 011915 (2008)] to 100% [in Molecular Motors, edited by M. Schliwa (Wiley-VCH Verlag GmbH, Weinheim (2003), p. 207]. In this note we attemp to clarify the issues involved. We also find an upper bound on the kinesin efficiency by constructing an ideal kinesin cycle to which the real cycle may be compared. The ideal cycle has a thermal efficiency of less than one, and the real one is less efficient than the ideal one always, in compliance with Carnot’s theorem.